HFC-23을 포함한 2성분계 CFC대체 혼합냉매의 상평형

박기현, 임종성, 이윤우, 김재덕, 이창하*

한국과학기술연구원 환경공정연구부

연세대학교 화학공학과*

Phase Equilibria of Binary Mixtures of CFC Alternative Refrigerant Containing HFC-23

Ki-Hyun Park, Jong-Sung Lim, Youn-woo Lee, Jae-Duck Kim, Chang-Ha Lee*

Environment and Process Technology Division, KIST

Dept. of Chem. Eng., Yonsei University*

Introduction

Chlorofluorocarbons (CFCs) have been widely used as refrigerants, blowing agents, propellants, or cleaning agents due to their outstanding properties.  However, production and use of CFCs are currently being phased out under the international Montreal Protocol agreement because of global environmental concerns.  HFC mixtures have been considered as promising candidates for replacement of CFC compounds since their ozone depletion potentials are low. Vapor-liquid equilibrium data are required as one of the most important types of information in evaluating the performance of refrigeration cycles and determining their optimal compositions. In this work, we measured VLE data for two binary systems of Trifluoromethane(HFC-23) + 1,1,1,2-Tetrafluoroethane (HFC-134a) and  Trifluoromethane(HFC-23) + 1,1,1,2,3,3,3- Heptafluoropropane (HFC-227ea) at 283.15 and 293.15K, respectively. Experimental data were correlated with the Peng-Robinson equation of state[1] using the Wong and Sandler mixing rule[2]

Theory

The VLE data were correlated with the Peng-Robinson equation of state. The Peng-Robinson equation of state is expressed as follows

[eqn: P= {RT} over {v-b}- {a(T) } over {v(v+b)+b(v-b) }]	(1)

with

a(T)=(0.457232R2Tc2/Pc)□(T)	(2)

b=0.0077796RTc/Pc	(3)

□(T)=[1+□(1-T□0.5)]2	(4)

□=0.37464+1.54226□-0.26992□2	(5)

and where the parameter a is a function of temperature, b is constant, □ is a constant characteristic of each substance, □ is the acentric factor.

The Wong-Sandler mixing rule was used in this work to obtain equation of state parameters for a mixture from those of the pure components. This mixing rule for a cubic equation of state can be written as

[eqn: {b}_{m}= { SUM from { i } SUM from { j } { x}_{i }{ x}_{j }{(b-a/RT) }_{ ij}} over {(1- {A }`_{∞} ^{E }/CRT- SUM from { i } { x}_{i } { a}_{i }/RT { b}_{i } ) }]	(6)

with

(b-a/RT)ij=[eqn: { 1} over {2 }][(b-a/RT)i+(b-a/RT)j](1-kij)	(7)

and

[eqn: { {a }_{m } } over { {b }_{ m} } = SUM from { i } {x }_{ i}{ {a }_{i } } over { {b }_{ i} }+ { { A}`_{∞ } ^{E } } over {C }]	(8)

and where C is a numerical constant equal to [eqn: ln( SQRT { 2} -1)/SQRT { 2}] for the Peng- Robinson equation used in this work. Also, [eqn: { A}`_{ inf } ^{E }] is an excess Helmholtz free energy model at infinite pressure which can be equated to a low-pressure excess Gibbs free energy model[3]; in this study we use the NRTL model[4] given by

[eqn: { { A}`_{∞ } ^{ E} } over {RT } = SUM from { i } { x}_{i } { SUM from { j } { x}_{j} { G}_{ji} {tau }_{ji}} over { SUM from { k } { x}_{k} { G}_{ki} }]	(9)

with

Gji=exp(-□ij□ji)  and □ij = Aij/RT	(10)

where Gji is the local compositon factor for NRTL model, □ijis the NRTL model binary interaction parameter, Aij=(gij - gji) and gij is an interaction energy parameter of the i-j, □ij is a non-randomness parameter and R is the universal gas constant (8.314 JK-1mol-1). We have set the non-randomness parameter,□ij, equal to 0.3 for all the binary mixtures studied here.  The Marquardt algorithm was applied to obtain the parameters with the following objective function:

objective function =[eqn: { { 1} over {N } SUM from {j} to {n} LEFT [ LEFT ( { { P}_{j,exp}-{ P}_{j,cal} } over {{ P}_{j,exp} } RIGHT ) TIMES 100RIGHT ] }^{ 2}]	(11)

Experimental Procedure

Experiments for a binary system were performed by the following procedure.  The whole system was evacuated by a vacuum pump to remove all the inert gases.  A certain amount of HFC-134a(or HFC-227ea) was introduced into the cell, and then the temperature of the entire system was maintained constant by controlling the temperature of the water bath.  After the desired temperature was attained, the pressure of the pure component was measured.  A proper amount of HFC-23 was supplied to the cell from a charging cylinder.  The mixture in the cell was stirred continuously by the magnetic stirrer for over 1 hour.  Both vapor and liquid phases were recirculated by the high-pressure pump until the equilibrium state was established. It is believed that 1 hr or more is sufficient to obtain thermal equilibrium between the cell fluid and the thermostated bath.  After 1 hr or more from the beginning, pressure was measured and then vapor and liquid samples were taken from the recycling lines by the vapor and liquid sampling valves, respectively.  The composition of the samples were measured by immediately injecting them into the gas chromatograph which is connected on-line to both vapor and liquid sampling valves. The gas chromatograph was calibrated with pure components of known purity and with mixtures of known composition that were prepared gravimetrically. The composition uncertainty of the liquid and vapor phase composition is estimated to be within  0.5 mol%, including the uncertainty of the calibration curve

Table 1. Comparison of the Measured Pure Components Vapor Pressures with the Calculated values from the Database REFPROP 6.01 (1998)

component	T/K	P/Mpa		△Pa/MPa	△P/Pb/(%)
		measd	calcd
HFC-23	283.15	3.2800	3.2740	0.0060	0.183
	293.15	4.2029	4.2020	0.0009	0.021
HFC-134a	283.15	0.4158	0.4146	0.0012	0.289
	293.15	0.5736	0.5717	0.0019	0.331
HFC-227ea	283.15	0.2803	0.2797	0.0006	0.214
	293.15	0.3905	0.3891	0.0014	0.358

△Pa=[eqn: LEFT | { P}_{exp}- { P}_{cal } RIGHT |], and △Pb/P=[eqn: LEFT |LEFT({P}_{exp}- {P}_{cal}/ {P}_{exp} RIGHT) RIGHT| times 100]

Results and Discussion

Table 1 is a comparison of measured vapor pressures of pure HFC-23, HFC-134a and HFC-227ea with those calculated from the database REFPROP 6.01[5] which is considered to be reliable for the pure compounds. The average deviation (|□P|/P) between measured and calculated values from the data of REFPROP 6.01 is 0.102% for HFC-23, 0.310% for HFC-134a and 0.286% for HFC-227ea. We measured mole fraction of the liquid and vapor phases, pressures, and temperatures in equilibrium and the deviations between measured and calculated pressures (△P/P) and vapor compositions(△y), point by point.  Table 2 lists the interaction parameters of binary mixtures for each isotherm, the binary parameters of the NRTL model with Wong-Sandler mixing rules, and the average deviations of pressure (□P/P) and vapor phase composition (□y) between measured and calculated values.  As can be seen in Table 2, the average deviations of pressures are 0.5215% for the HFC-23 + HFC-134a  system and 1.170% for the HFC-23 + HFC-227ea system and those of vapor phase compositions are 0.0102 for the HFC-23 + HFC-134a system and 0.0083 for the HFC-23 + HFC-227ea system.  Figure 1 and 2 show the comparison of measured and calculated values with a P-R equation of state for HFC-23 + HFC-134a and HFC-23 + HFC-227ea at 283.15 and 293.15 K. From these figures and the low average deviations of pressure (<1.17%) and

Table 2. Values of Binary Parameters and Average Deviations of P and y

System	T/K	NRTL parameters/kJ·mol-1			□Pc/(%)	□yd
HFC-23/HFC-134a	283.15	Kij=0.253	Aij=0.420	Aji=-0.302	0.666	0.0117
	293.15	Kij=0.243	Aij=0.869	Aji=-0.913	0.377	0.0088
HFC-23/HFC-227ea	283.15	Kij=0.635	Aij=3.829	Aji=-2.420	0.885	0.0093
	293.15	Kij=0.644	Aij=-1.395	Aji=1.264	1.455	0.0074

□Pc=[eqn: { 1} over {N } SUM LEFT | LEFT ( { P}_{exp }- { P}_{cal } RIGHT )/{ P}_{exp } RIGHT | TIMES 100], and □yd=[eqn: { 1} over {N } SUM LEFT | { y}_{exp } - { y}_{ cal} RIGHT |]

vapor phase compositions (<0.0102) in Table 2, we conclude that the values calculated with the P-R equation of state and Wong-Sandler mixing rules give comparatively good agreement with experimental data.  Both isothermal systems exhibit no azeotropes.

Literature Cited

1. Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59-64.

2. Wong, D. S. H.; Sandler, S. I.. A Theoretically Correct Mixing Rule for Cubic Equation of State.  AIChE J. 1992, 38, 671-680.

3. Wong, D. S. H.; Orbey, H.; Sandler, S. I. An Equation of State Mixing Rule for Nonideal Mixtures using Available Activity Coefficient Model Parameters and Which Allows Extrapolation over Large Ranges of Temperature and Pressure. Ind. Eng. Chem. Res. 1992, 31, 2033-2039.

4. Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Func- tions for Liquid Mixtures. AIChE J. 1968, 14, 5-144.

5. Huber, M.; Gallagher, J., McLinden, M. O., Morrison, G., REFPROP, V.6.01, NIS T.(1998)